External hard disk takes a long time to show up

What file systems are on these external drives?

Run the third party app EtreCheck and post the report here so we an examine it for clues.

Make sure to disconnect all other external devices in case one of them is causing a problem.

If the drives are using a native macOS file system such as HFS+ (aka MacOS Extended), APFS, exFAT, or even FAT32 (aka "msdos"), then you can try booting into Safe Mode to see how those drives mount. Unfortunately if a drive is using the NTFS file system Safe Mode is not an option if you were using a third party NTFS driver (or the manufacturer's proprietary drive software to manage the drive) since the third party NTFS drivers seem to modify macOS to default to using the third party driver which is not available in Safe Mode.

FYI, not all external devices are compatible with an Apple Silicon M-series Mac. I know when the Apple Silicon Macs were first released that a Samsung T5 v1 SSD would not work, but a v2 model would. I have no idea if Apple ever resolved those issues or if they still exist. I personally experienced this compatibility issue with a device on my M1 Mac in 2020, but never bothered to try it again after later OS updates/upgrades and system firmware updates.